Multiplying the common ordinary fractions: 64/111 × - 86/104 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
64/111 × - 86/104 = ?
Simplify the operation
Rewrite the equivalent simplified operation:
Combine the signs of the fractions into a single one, placed in front of the expression. If the sign is + then it is usually not written.
The sign of a multiplication operation:
+ 1 × + 1 = + 1
+ 1 × - 1 = - 1
- 1 × - 1 = + 1
64/111 × - 86/104 =
- 64/111 × 86/104
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.
* By reducing the values of the numerators and the denominators of the fractions the calculations are easier to make.
A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.
* In order to easily reduce a fraction, factor its numerator and denominator. This way all the common prime factors are easily identified and crossed out, without calculating the GCF.
64/111 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
64 = 26
111 = 3 × 37
86/104 =
(2 × 43)/(23 × 13) =
((2 × 43) ÷ 2)/((23 × 13) ÷ 2) =
(2 ÷ 2 × 43)/(23 ÷ 2 × 13) =
(1 × 43)/(2(3 - 1) × 13) =
(1 × 43)/(22 × 13) =
43/52
Rewrite the equivalent simplified operation:
- 64/111 × 86/104 =
- 64/111 × 43/52
Perform the operation of calculating the fractions
Multiply the fractions:
1) Multiply the numerators, that is, all the numbers above the fractions bars, separately.
2) Multiply the denominators, that is, all the numbers below the fractions bars, separately.
* Factor all the numerators and all the denominators in order to easily reduce (simplify) the end fraction.
- 64/111 × 43/52 =
- (64 × 43) / (111 × 52) =
- (26 × 43) / (3 × 37 × 22 × 13) =
- (26 × 43) / (22 × 3 × 13 × 37)
Fully reduce (simplify) the end fraction to its lowest terms equivalent:
Calculate the greatest common factor, GCF,
of the numerator and denominator of the fraction:
A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.
To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.
* To calculate the GCF, we need to factor the numerator and the denominator of the fraction into prime factors.
Then multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).
GCF (26 × 43; 22 × 3 × 13 × 37) = 22
Divide the numerator and the denominator by their GCF:
- (26 × 43) / (22 × 3 × 13 × 37) =
- ((26 × 43) ÷ 22) / ((22 × 3 × 13 × 37) ÷ 22) =
- (26 ÷ 22 × 43)/(22 ÷ 22 × 3 × 13 × 37) =
- (2(6 - 2) × 43)/(2(2 - 2) × 3 × 13 × 37) =
- (24 × 43)/(20 × 3 × 13 × 37) =
- (24 × 43)/(1 × 3 × 13 × 37) =
- (24 × 43)/(3 × 13 × 37) =
- (16 × 43)/(3 × 13 × 37) =
- 688/1,443
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 688/1,443 =
- 688 ÷ 1,443 ≈
- 0.476784476784 ≈
- 0.48
As a percentage:
A percentage value p% is equal to the fraction: p/100, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.
To do that, multiply the number by the fraction 100/100.
The value of the fraction 100/100 = 1, so by multiplying the number by this fraction the result is not changing, only the form.
- 0.476784476784 =
- 0.476784476784 × 100/100 =
( - 0.476784476784 × 100)/100 =
- 47.678447678448/100 ≈
- 47.678447678448% ≈
- 47.68%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
64/111 × - 86/104 = - 688/1,443
As a decimal number:
64/111 × - 86/104 ≈ - 0.48
As a percentage:
64/111 × - 86/104 ≈ - 47.68%
How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.
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